1. Field of the Invention
The present invention relates to a charged particle beam drawing apparatus and method, wherein patterns are drawn by a charged particle beam in a resist which is applied to an upper surface of a mask substrate.
2. Description of Related Art
As is known in the prior art, a charged particle beam drawing apparatus has a drawing chamber including a movable stage which supports a mask. The mask is formed by applying a resist to an upper surface of a mask substrate. In the charged particle beam drawing apparatus in the prior art, a charged particle beam is applied from an optical column to the resist for drawing patterns in the resist, and a dose of the charged particle beam applied from the optical column to the resist is corrected on the basis of proximity effect and fogging effect. For example, the charged particle beam drawing apparatus in the prior art is described in Japanese Unexamined Patent Publication No. 2007-220728.
In the charged particle beam drawing apparatus described in Japanese Unexamined Patent Publication No. 2007-220728, a proximity effect correction dose is calculated on the basis of equations 3, 4 described in Japanese Unexamined Patent Publication No. 2007-220728, and a fogging effect correction dose is calculated on the basis of an equation 15 described in Japanese Unexamined Patent Publication No. 2007-220728. Then, a correction dose of the charged particle beam applied from the optical column to the resist is calculated on the basis of an equation 2 described in Japanese Unexamined Patent Publication No. 2007-220728, the equation 2 multiplies the proximity effect correction dose by the fogging effect correction dose.
An equation 1 described in Japanese Unexamined Patent Publication No. 2007-220728, shows a relation between an accumulation dose of the charged particle beam accumulated in the resist considering proximity effect and fogging effect, and an accumulation energy (absorption amount of the resist) of the charged particle beam accumulated in the resist. In detail, the left side of the equation 1 described in Japanese Unexamined Patent Publication No. 2007-220728, corresponds to the accumulation energy of the charged particle beam accumulated in the resist, and the right side of the equation 1 described in Japanese Unexamined Patent Publication No. 2007-220728, corresponds to the accumulation dose of the charged particle beam accumulated in the resist considering proximity effect and fogging effect.
In the charged particle beam drawing apparatus described in Japanese Unexamined Patent Publication No. 2007-220728, a ratio of the accumulation energy of the charged particle beam accumulated in the resist (which corresponds to the left side of the equation 1 of Japanese Unexamined Patent Publication No. 2007-220728), to the accumulation dose of the charged particle beam accumulated in the resist considering proximity effect and fogging effect (which corresponds to the right side of the equation 1 of Japanese Unexamined Patent Publication No. 2007-220728) is a constant. In detail, the constant is 1 in the equation 1 of Japanese Unexamined Patent Publication No. 2007-220728.
A following equation (1) corresponds to the equation 1 of Japanese Unexamined Patent Publication No. 2007-220728. The equation (1) shows a relation between the accumulation energy of the charged particle beam accumulated in the resist and the accumulation dose of the charged particle beam accumulated in the resist considering proximity effect and fogging effect, in the typical charged particle beam drawing apparatus in the prior art.
                                                                        E                ⁡                                  (                  x                  )                                            =                            ⁢                              K                [                                                                            D                      ⁡                                              (                        x                        )                                                              2                                    +                                      η                    ⁢                                                                  ∫                        A                                            ⁢                                                                        D                          ⁡                                                      (                                                          x                              ′                                                        )                                                                          ⁢                                                                              g                            p                                                    ⁡                                                      (                                                          x                              -                                                              x                                ′                                                                                      )                                                                          ⁢                                                  ⅆ                                                      x                            ′                                                                                                                                +                                                                                                                      ⁢                              θ                ⁢                                                      ∫                    A                                    ⁢                                                            D                      ⁡                                              (                                                  x                          ′                                                )                                                              ⁢                                                                  g                        F                                            ⁡                                              (                                                  x                          -                                                      x                            ′                                                                          )                                                              ⁢                                          ⅆ                                              x                        ′                                                                                                        ]                                                                          =                            ⁢              C                                                          (        1        )            
In detail, the equation (1) shows the relation between the accumulation energy E(x) in a position x on a line extending in x axis direction, of the charged particle beam accumulated in the resist, and the accumulation dose of the charged particle beam accumulated in the resist considering proximity effect and fogging effect. The accumulation dose of the charged particle beam accumulated in the resist considering proximity effect and fogging effect, corresponds to a phrase in square brackets [ ] on the right side of the equation (1).
In the equation (1), K is a conversion coefficient from the accumulation dose of the charged particle beam accumulated in the resist, to the accumulation energy E(x) of the charged particle beam accumulated in the resist. That is, K shows a ratio of the accumulation energy E(x) of the charged particle beam accumulated in the resist, to the accumulation dose of the charged particle beam accumulated in the resist. C is a threshold of the accumulation energy E(x) of the charged particle beam accumulated in the resist.
In the equation (1), D(x) shows the dose of the charged particle beam applied from the optical column to the position x in the resist. A left end portion (D(x)/2) in square brackets [ ] on the right side of the equation (1) shows the accumulation dose of the charged particle beam accumulated in the position x in the resist. Namely, the equation (1) means that a half (D(x)/2) of the dose D(x) of the charged particle beam applied from the optical column to the position x in the resist is accumulated in the position x in the resist.
A middle portion in square brackets [ ] on the right side of the equation (1) shows the accumulation dose of the charged particle beam accumulated in the position x in the resist by proximity effect, after the charged particle beam is applied from the optical column to a position x′ in a whole drawing area A in the resist. In detail, in the equation (1), η shows a proximity effect correction coefficient, and gP shows a proximity effect influence distribution. In the typical charged particle beam drawing apparatus in the prior art, Gaussian distribution (normal distribution) is used as the proximity effect influence distribution gP.
A right end portion in square brackets [ ] on the right side of the equation (1) shows the accumulation dose of the charged particle beam accumulated in the position x in the resist by fogging effect, after the charged particle beam is applied from the optical column to the position x′ in the whole drawing area A in the resist. In detail, in the equation (1), θ shows a fogging effect correction coefficient, and gF shows a fogging effect influence distribution. In the typical charged particle beam drawing apparatus in the prior art, Gaussian distribution (normal distribution) is used as the fogging effect influence distribution gF.
In the charged particle beam drawing apparatus, if a base dose of the charged particle beam (see paragraph 0085 of Japanese Unexamined Patent Publication No. 2007-220728) is applied from the optical column to the resist without considering proximity effect and fogging effect, in order to draw linear patterns PL1, PL2, PL3 (see FIG. 5) in the resist of the mask M (see FIG. 5), and to make the width W (see FIG. 5) of the linear patterns PL1, PL2, PL3 uniform, the width W (the vertical axis of the graph in FIG. 6) of the linear pattern PL2 in positions x3, x4 (see FIGS. 5 and 6) around which the pattern density is high, is larger than the width W (the vertical axis of the graph in FIG. 6) of the linear patterns PL1, PL3 in positions x1, x6 (see FIGS. 5 and 6) around which the pattern density is low, under the influence of proximity effect and fogging effect.
Accordingly, in the charged particle beam drawing apparatus in the prior art, the accumulation dose of the charged particle beam accumulated in the resist (in square brackets [ ] on the right side of the equation (1)) in each position, such as positions x1, x2, x3, x4, x5, x6 (see FIGS. 5 and 6) is adjusted so as to make the width W (the vertical axis of the graph in FIG. 6) of the linear pattern PL2 in the positions x3, x4 (see FIGS. 5 and 6) around which the pattern density is high, and the width W (the vertical axis of the graph in FIG. 6) of the linear patterns PL1, PL3 in the positions x1, x6 (see FIGS. 5 and 6) around which the pattern density is low, equal.
In detail, in the charged particle beam drawing apparatus in the prior art, the conversion coefficient K in the equation (1) is not changed, but is a constant, and the accumulation dose of the charged particle beam accumulated in the resist (in square brackets [ ] on the right side of the equation (1)) in each position x, such as the positions x1, x2, x3, x4, x5, x6 (see FIGS. 5 and 6) is adjusted, so as to make a value of the accumulation energy E(x) of the charged particle beam accumulated in the resist (on the right side of the equation (1)) equal to the threshold C.
The inventor's studies show that if the patterns PL1, PL2, PL3 (see FIG. 5) are drawn in the resist of one type of mask, the width W (the vertical axis of the graph in FIG. 6) of the linear pattern PL2 in the positions x3, x4 (see FIGS. 5 and 6) around which the pattern density is high, and the width W (the vertical axis of the graph in FIG. 6) of the linear patterns PL1, PL3 in the positions x1, x6 (see FIGS. 5 and 6) around which the pattern density is low, can be made equal, by adjusting the accumulation dose of the charged particle beam accumulated in the resist (in square brackets [ ] on the right side of the equation (1)) in each position x, such as the positions x1, x2, x3, x4, x5, x6 (see FIGS. 5 and 6). Namely, the inventor's studies show that critical dimension (CD) uniformity of the type of mask can be improved. However, the inventor's studies show that if the patterns PL1, PL2, PL3 (see FIG. 5) are drawn in the resist of another type of mask, it is difficult to make the width W (the vertical axis of the graph in FIGS. 7 and 8) of the linear pattern PL2 in the positions x3, x4 (see FIGS. 5, 7 and 8) around which the pattern density is high, and the width W (the vertical axis of the graph in FIGS. 7 and 8) of the linear patterns PL1, PL3 in the positions x1, x6 (see FIGS. 5, 7 and 8) around which the pattern density is low, equal by adjusting the accumulation dose of the charged particle beam accumulated in the resist (in square brackets [ ] on the right side of the equation (1)) in each position x, such as the positions x1, x2, x3, x4, x5, x6 (see FIGS. 5, 7 and 8).